The logic of beginning and ending

Abstract

A very special chapter of Medieval logic was opened when philosophers of that time took up the analysis of the verbs ‘incipit’ (it begins) and ‘desinit’ (it ends). The starting point was found in Aristotle’s Physics, books 6 and 8, so it was no coincidence that their deliberations proved to be relevant not only to logic but also to physics. The questions concerning beginning and ending naturally led to the consideration of temporal limits. The number of Medieval logicians who worked on these questions was very large [Kretzmann, 1976, pp.101ff]. As pointed out by William and Martha Kneale [1962, p.233–34], the very fact that so much attention was given to this type of problem constitutes an excellent proof of the formal character of Medieval logic. The general problem had to do with the correct understanding of ‘incipit-statements’ such as:

• (1) ’socrates begins to be white’,

• (2) ’socrates begins to run’,

and analogously for statements containing the verb ‘desinitrs. The task of the logician was to give clear semantic definitions of ‘incipit’ (‘begins’) and lsdesinit’ (‘ends’). The most common definition given in order to clarify the meaning of the aove examples was the following:

• (1′) ’socrates is white and was not white immediately before’

• (2′) ’socrates does not run, but will run immediately after’